Woven wire systems have been used with vibratory machines for screening various materials. Woven wire systems typically have a steel or other metal woven wire mesh screen or wire cloth that is tensioned over a plurality of frame members (e.g., bucker bars) across the entire width of a vibratory machine. Replacement of the woven wire screen due to, for instance, damage and/or wear and tear, can require removal and replacement of the entire woven wire screen. This can be an expensive and time consuming process. Efforts have been made to replace woven wire systems with modular screening systems that allow for removal and replacement of single individual modular screen panels. However, such efforts have been difficult due to the excessive weight of frames that may need to be installed on the portable vibratory machine to accommodate the modular screen panels and due to need for structural modifications of the vibratory machine that may be undesirable.